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How many prime numbers between 1 and 100 are factors of 7,15

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avigutman

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26 Jan 2023, 07:36

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Video solution from Quant Reasoning:
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Thib33600

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26 Jan 2024, 16:55

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Bunuel

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Hate to play devil's advocate here, but the question doesn't clarify how many UNIQUE prime numbers are factors of 7150. (Which would change the answer to five). Am I missing something?

How many prime numbers between 1 and 100 are factors of 7,150?
A. One
B. Two
C. Three
D. Four
E. Five

Make prime factorization of 7,150 --> 7,150=2*5^2*11*13. So 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150 (you shouldn't count one prime factor twice).

Answer: D.

Tips to be able to find factors of 7,150 fast?

because i find 715 * 10 = 715 * 2 *5 but then finding for 715 takes me too much time.

thanks

Bunuel

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27 Jan 2024, 00:48

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Thib33600

Bunuel

jgonza8

Hate to play devil's advocate here, but the question doesn't clarify how many UNIQUE prime numbers are factors of 7150. (Which would change the answer to five). Am I missing something?

Tips to be able to find factors of 7,150 fast?

because i find 715 * 10 = 715 * 2 *5 but then finding for 715 takes me too much time.

thanks

Have you checked this post?

To address your question, since the units digit of 715 is 5, it is divisible by 5: 715/5 = 143. Now, since 130 is divisible by 13, then so is 130 + 13 = 143: 143/13 = 11.

Hope it helps.

e3thekid

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26 Jul 2024, 20:47

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seofah

How many prime numbers between 1 and 100 are factors of 7,150?

A. One
B. Two
C. Three
D. Four
E. Five

Prime factorization of 7150:
715 x 2 x 5
5 x 143 x 2 x 5
5 x 11 x 13 x 2 x 5

2 x 5^2 x 11 x 13

Prime number factors of 7150:
2,5,11,13 -> four factors between 1 and 100 that are prime

Option D

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NEYR0N

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24 Mar 2025, 11:44

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KarishmaB, isn't 'which' prime numbers more appropriate? I still can't understand how unique is implied here.

KarishmaB

jgonza8

Hate to play devil's advocate here, but the question doesn't clarify how many UNIQUE prime numbers are factors of 7150. (Which would change the answer to five). Am I missing something?

Yes, you are! Read the question again:
How many prime numbers between 1 and 100 are factors of 7,150?

The prime numbers between 1 and 100 are 2, 3, 5, 7, 11, 13, 17, 19... etc

5 appears only once between 1 and 100 so there is absolutely no confusion. Out of these 25 prime numbers, only 4 are factors of 7150: 2, 5, 11 and 13

KarishmaB

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24 Mar 2025, 21:41

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But if you want to know just the total number and not which ones, how will you phrase it? Between 1 and 100, there are 25 prime numbers. How many of them are factors of 7150? There is only one 5 between 1 and 100. You will count it only once. This is one way of ensuring that you count only unique factors without needing to write "distinct". Though in any case, almost always the question asks about "distinct" factors.
I don't remember counting a factor twice because it appears twice in a prime factorization in any official question. I obviously would not go on to say that it cannot happen, but it would be rare and truth be told, I am not sure how I would phrase a question that would want you to answer 3 when asked about the number of prime factors of 12. Perhaps something on the lines of: N prime numbers are multiplied to give 12. What is N?

INprimesItrust

KarishmaB, isn't 'which' prime numbers more appropriate? I still can't understand how unique is implied here.

KarishmaB

jgonza8

Hate to play devil's advocate here, but the question doesn't clarify how many UNIQUE prime numbers are factors of 7150. (Which would change the answer to five). Am I missing something?